## 1. Introduction

[2] The Global Positioning System (GPS) is a useful tool for the measurement of the ionospheric total electron content (TEC). A GPS satellite broadcasts dual-frequency signals (*f*_{1} = 1575.42 MHz and *f*_{2} = 1227.60 MHz) to allow users to derive the ionospheric delays. The measured differential delays, however, contain not only the delay due to the ionospheric TEC, but also the delay generated by interior electronic circuits of the GPS satellite transmitters and ground receivers. The latter delay is referred to as instrumental bias (or interfrequency bias). Therefore, for the purpose of accurate measurement of TEC, we have to remove these instrumental biases. Several methods have been proposed for determination of the instrumental biases. Among them most methods assume a rather smooth spatial and temporal variation of the ionospheric behavior over the observation area during several hours of observation. *Lanyi and Roth* [1988] proposed a method in which the vertical TEC is modeled by a quadratic function of latitude and longitude of two-dimensional position under consideration. In this method, GPS observation data obtained during a night in a midlatitude area from a single GPS receiver are used to estimate the coefficients of a two-dimensional quadratic model (by using the least squares method), and at the same time, satellite and receiver biases are derived. *Coco et al.* [1991] used this method to investigate the general tendency of the variability of the GPS instrumental biases. To improve the accuracy of the bias estimation, *Wilson et al.* [1992, 1995] extended single-site technique proposed by *Lanyi and Roth* [1988] to a multisite one by modeling a global vertical TEC by two-dimensional spherical harmonics. They applied this technique to obtain the diurnal and semidiurnal average of the ionospheric TEC map of the Northern Hemisphere by using data from a global network of GPS stations. An approach based on the Kalman filtering technique was proposed by *Sardon et al.* [1994], which uses a second-order polynomial approximation for TEC over each station in a local reference frame. In this method instrumental biases and TEC are estimated by using stochastic parameters in the Kalman filter. These methods assume a smoothly varying ionosphere over the observation area during several hours so that the TEC can be modeled with a lower-order polynomial.

[3] The GPS Earth Observation Network (GEONET) [*Miyazaki et al.*, 1997] installed by the Geographical Survey Institute of Japan (GIS) has densely located receivers covering Japan (more than 1000 receivers) and allows derivation of TEC with high spatial resolution. *Otsuka et al.* [2002] developed a technique to remove instrumental biases with a least squares fitting procedure and construct two-dimensional maps of the absolute TEC over Japan by using GPS data of GEONET. Although this method can be derived the TEC maps over Japan with considerably high spatial and temporal resolutions, the error becomes more noticeable with lowering latitude of the observation areas because of the assumption that the hourly average of vertical TEC is uniform within an area covered by a receiver. The area covered by a receiver approximately corresponds to the surrounding 1000 km, so this method should be applied carefully to data collected the lower latitudes where large ionospheric variability exists. Differently from the method of *Otsuka et al.* [2002], *Ma and Maruyama* [2003] developed a method in which both the biases and TECs are determined at the same time by using GPS data from GEONET collected within one day. This method is based on the assumption that TEC is uniform in a small area (2 by 2 in latitude and longitude, respectively), and the TECs and biases of the satellites and receivers are determined by using the least squares fitting technique. Both methods are applicable only in those regions where a network of densely located receivers, such as GEONET, has been established. Thus a simple method to estimate a single receiver bias was proposed by *Ma and Maruyama* [2003], in which the satellite biases determined from GEONET were used. However, because the estimation error tends to increase at lower latitudes; the simple method should be applied at lower latitudes (<30°*N*) where a great latitudinal TEC gradient and the equatorial anomaly exist. It is, therefore, still difficult to determine the receiver bias when a receiver is located in a low-latitude area.

[4] Another large error source in previous studies stems from the assumption of a thin shell, where electrons lie in an infinitely thin ionosphere located at a constant height above the Earth. There are two major drawbacks to estimation of TEC by using the thin-shell model. First, the height of the ionospheric layer is commonly chosen at a fixed height (e.g., 400 km altitude), whereas the actual ionospheric layer is changeable depending on season, latitude, local time, etc. The height of the ionospheric layer should be precisely estimated before an accurate measurement of the TEC values. Second, at the low latitudes (in the vicinity of the geomagnetic equator) the spatial changes in TECs are too drastic to be expressed by the thin-shell model. Methods based on the thin-shell model are therefore not very applicable to analyses of the ionosphere near the geomagnetic equator.

[5] In order to cope with the above problems we propose an alternative method for determination of the receiver biases by using RMTNN [*Liaqat et al.*, 2003]. In this method we reconstruct an approximate three-dimensional electron distribution as a computer tomographic image [*Ma et al.*, 2000] and determine the biases of the ground receivers from the observation data by making use of the excellent capability of the multilayer neural network to approximate an arbitrary function. We successfully applied this method which does not rely on the assumption of a thin shell, to both the model data and the observation data analyses.

[6] The neural network parameter estimation method is described in section 2, where, we summarize the basics and features of a multilayer neural network. Numerical experiments for model problem are presented in section 3. In section 4, we evaluate the proposed method on the real observation data. Section 5 has a summary of the paper and mentions future work.